Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1166 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #21424091 | C2 | semidirect |
| 6. #21423891 | C2 | semidirect |
| 150. C59 | #20730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837879 | 2 |
| #21432731 | 2 |
| #21424179 | 2 |
| #21424091 | 2 |
| #21424019 | 2 |
| #21423891 | 2 |
| C59×#1822 | 2 |
| #20730 | 59 |